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Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in Mathematica. The program condens.m automatically carries out the…
Unsupervised domain mapping has attracted substantial attention in recent years due to the success of models based on the cycle-consistency assumption. These models map between two domains by fooling a probabilistic discriminator, thereby…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
In a non supervised Bayesian estimation approach for inverse problems in imaging systems, one tries to estimate jointly the unknown image pixels $f$ and the hyperparameters $\theta$ given the observed data $g$ and a model $M$ linking these…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
The problem of computing posterior functionals in general high-dimensional statistical models with possibly non-log-concave likelihood functions is considered. Based on the proof strategy of Nickl and Wang (2022), but using only local…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…
A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
High-dimensional linear and nonlinear models have been extensively used to identify associations between response and explanatory variables. The variable selection problem is commonly of interest in the presence of massive and complex data.…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, as basket analysis, these models may be seen as a constrained version of…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…